which is followed by a finite size cutoff. The value of the exponent is rather high \(\tau =3.4\pm 0.1\)  in
agreement with former studies of the fiber bundle model [1]}, [2]}, [3]}. The rapidly decreasing distribution and the low cutoff burst size \(\Delta _{max}\)  clearly show that cascades are typically small compared to the system size \(N\) . Due to the strong localization large avalanches would lead
to immediate collapse of the bundle on the regular lattice.
However, increasing the fraction of long range connections by increasing the rewiring probability \(p\) ,
the stress localization gets gradually reduced, hence, the system can tolerate larger and
larger failure cascades without suffering catastrophic collapse.
As a consequence, the cutoff burst size \(\Delta _{max}\)  increases and the distribution \(p(\Delta )\) 
exhibits a crossover to a second power law regime
with a lower exponent. The smaller value of \(\tau \)  shows the growing fraction of large size
cascades in the failure dynamics of the system (see Fig. REF ).
<FIGURE>